Question

Flying with the wind, a plane can fly 900 miles in 6 hours. Against the wind, the plane can fly the same distance in 10 hours. What is the rate of the wind ?

Answer 1

Given:

Flying with the wind, a plane can fly 900 miles in 6 hours.

Let the speed of the plane = x

Let the speed of the wind = y

Speed = distance/time

So,

$\begin{gathered} x+y=\frac{900}{6} \\ x+y=150\rightarrow(1) \end{gathered}$

Against the wind, the plane can fly the same distance in 10 hours.

So,

$\begin{gathered} x-y=\frac{900}{10} \\ x-y=90\rightarrow(2) \end{gathered}$

Solving the equations (1) and (2):

$\begin{gathered} x+y=150 \\ x-y=90 \\ ======= \\ 2x=240 \\ x=\frac{240}{2}=120 \\ y=150-x=150-120=30 \end{gathered}$

So, the rate of the wind = 30 miles per hour